Ray Tracing Based on Interpolation of Visibility of Point Light Sources

In this paper, Whitted-style ray tracing is considered. Its particular features are: only point or directional light sources and only sharp shadows. Nevertheless, it is the most popular algorithm of photorealistic rendering. One of its basic operation is a determination of visibility between two scene positions, especially between the light position and an object point: the so-called shadow ray. To speed up this, the following techniques were developed: direct calculation (shadow rays), the shadow map algorithm, the shadow volume algorithm, and the light meshes method. In order to enhance the realism of calculated images, a lot of developments were performed to modify the algorithm so that it could generate (or more exactly simulate) soft shadows instead of theoretical sharp ones. Each of techniques mentioned above was modified to produce soft shadows. Only a very slow approach based on the direct calculation of shadow rays (often called “area shadows”) works without drawbacks. The shadow map and volume techniques are very sensitive to the relative positions of light sources and objects in the scene. In this paper, we describe an original lights visibility grid algorithm which is also a modification of the classical Whitted algorithm. Note that our algorithm generates images with blurred sharp shadows, i.e., it generates soft shadows. It does not depend on relative positions of light sources and object points. It was shown both theoretically and by numerical experiments that if the rendering complexity (the number of objects, the number of lights, the image resolution) increases the computation time of our algorithm becomes even less than that of the Whitted algorithm.